Measurements Chapter 3

Measurements Chapter 3

Analytical Chemistry is the science of chemical measurement. Its object is the generation, treatment and evaluation of signals from which information is obtained on the composition and structure of matter.* Measurement is the process of obtaining the magnitude of a quantity. Example: The amount of saturated fat in the sample is 3 g/serving. Danzer, K. 2007. Analytical Chemistry: Theoretical and Metrological Fundamentals. Germany: Springer

Some definitions: The amount of saturated fat in the sample is 3 g/serving. QUANTITY is the attribute of phenomenon, body or substance that may be distinguished qualitatively and determined quantitatively. VALUE (of a quantity) is the magnitude of a particular quantity generally expressed as a unit of measurement multiplied by a number. UNIT (of measurement) is a particular quantity, defined and adopted by convention, with which other quantities of the same kind are compared in order to express their magnitudes relative to that quantity.

Globalization requires comparability of measurements.

Our current system of measurement is based on the Metric System. The Meter Convention led to the signing of the Treaty of the Meter (1875) establishing the Bureau International des Poids et Mesures (BIPM). In 1960, the 11th General Conference on Weights and Measures adopted the name Système International d'unités (International System of Units) for the recommended practical system of units of measurement.

The SI system is based on a set of seven fundamental or base units. Each unit is identified with a physical quantity.

The definition of each unit has evolved through time. The METER unit 1 st Definition: 1/10,000,000 the distance from the equator to the north pole 2 nd Definition: The distance between two fine lines engraved on a corrosion-resistant metal bar kept at the BIPM. 3 rd Definition: 1,650,763.73 wavelengths of orange-red light from electrically excited krypton atoms Current Definition: The distance travelled by light in a vacuum in 1/299,792,458 second.

The kg is the only remaining unit whose definition is based on an international prototype. Prototype No. 52, Germany Prototype No. 18, UK International Prototype (90% Pt and 10% Ir alloy) Sevres, France Prototype No. 20, US

Other units are derived from the SI base units.

To express fractions or multiples of the units (by the power of 10), it is convenient to use prefixes.

The AMOUNT OF SUBSTANCE is an SI fundamental quantity. It is the number of some specified elementary entity. 100 atoms of O 1 molecule of Glucose 18 e - But often times, since chemical particles are too small, the number are in large magnitude. The counting is made easier if expressed in terms of group of particles. 100 yrs = 1 century 12 pcs = 1 dozen 6.02 x 10 23 particles = 1 mole

Ways of Expressing Concentration Chapter 3

In measuring the amount of substance, the specie being measured is specified. In most cases, the amount of substance is expressed relative to the amount, mass or volume of the matrix where the specie is being determined. One serving of milk contains 195 mg phosphorus. matrix value unit specie/analyte CONCENTRATION refers to how much solute is contained in a given mass or volume. The matrix could be homogeneous or heterogeneous mixture.

Concentration can be expressed in many forms. Concentration Definition Unit Molarity Amount of substance in a liter of solution. mol/l (molar) Molality Weight percent Volume percent Mole fraction Amount of substance in a kilogram solvent Mass of substance per mass solution Volume of substance per volume solution Amount of substance in the total amount of solution mol/kg (molal) g/g% (wt %) vol% unitless

Ways of Expressing Concentration Mole Fraction (X) moles of A X A = sum of moles of all components Molarity (M) moles of solute M = liters of solution Molality (m) moles of solute m = mass of solvent (kg) Converting between molarity (M) and molality (m) requires density.

Sample Problem 1: Typical seawater contains 2.7 g NaCl per deciliter. What is the molarity of NaCl in the ocean? MgCl 2 has a typical concentration of 0.054 M in the ocean. How many grams of MgCl 2 are present in 25 ml of seawater.

Sample Problem 2: Find the molarity of HCl in a reagent labeled 37.0 wt % HCl, density = 1.188g/mL.

Other expressions of concentration: 1. Normality is the number of equivalence per liter solution. 2. Parts per million (ppm) is expressed in the units mg/ kg or µg/g. In aqueous solutions, ppm can also be expressed in the units mg/l or µg/ml. 3. Parts per billion (ppb) is expressed in the units µg/kg or ng/g. In aqueous solutions, ppb can also be expressed in the units µg/l or ng/ml.

Ways of Expressing Concentration Percent by Mass % by mass = mass of solute x 100% mass of solute + mass of solvent Parts per milion = mass of solute x 100% mass of solution ppm = mass of solute x 10 6 mass of solution

Parts per milion Ways of Expressing Concentration For dilute solutions (in the ppm and ppb level), density is almost equal to 1 g/ml ppm = mass of solute x 10 6 mass of solution ppm = g solute 1 g solution 1000 ml solution 1000 mg x x solute g solution ml x solution 1 L solution 1 g solute ppm = mg solute L solution

Sample Problem 3: A 0.1013 g oxalic acid, H 2 C 2 O 4, was dissolved in 250.0 ml water. What is the normality of this solution if used in a redox titration? (1 mole of H 2 C 2 O 4 gives 2 moles e - during the process).

Sample Problem 4: What is the normality of a 0.12 M solution of sulfuric acid, H 2 SO 4 : a. If it is used in an acid-base reaction? b. If it is used in a precipitation reaction to form BaSO 4.

Sample Problem 6: The concentration of C29H60 in summer rainwater is 34 ppb. Find the molarity of the compound in nanomoles/l (nm).

Preparation of solution is an essential part of a chemist s job. Different glassware are used according to the needed precision and accuracy of the solution to be prepared. The volumetric flask is a Tc glassware used to prepare solutions of exact concentration. DILUTION EQUATION M 1 V 1 =M 2 V 2

Sample Problem 7: Cupric Sulfate is commonly sold as pentahydrate, CuSO 4 5H 2 O. How many grams of this reagent should be dissolved in 250 ml volumetric flask to make a solution containing 8.00 mm Cu 2+.

Sample Problem 8: The solution of ammonia in water is called ammonium hydroxide because of the equilibrium NH 3 + H 2 O < -- > NH 4 + + OH - The density of concentrated ammonium hydroxide, which contains 28.0 wt% NH 3 is 0.899 g/ml. What volume of this reagent should be diluted to 500 ml to make 0.250 M NH 3.

Sample Problem 9: Drinking water usually contains 1.6 ppm fluoride (F - ) to prevent tooth decay. Consider a reservoir with a diameter 450 m and depth 10 m. a. How many liters of 0.10 M NaF should be added to produce 1.6 ppm F -? b. How many grams of solid NaF could be used instead?

Exercise 1) A solution is made by dissolving 13.5 g of glucose, C 6 H 12 O 6, in 0.100 kg of water. What is the mass percentage of solute in this solution? 2) A 2.5 g sample of ground water was found to contain 5.4 g of Zn 2+. What is the concentration of Zn 2+ in parts per million? 3) The solubility of MnSO 4 H 2 O in water at 20 C is 70 g per 100 ml of water. Is a 1.22 M solution of MnSO 4 H 2 O in water at 20 C saturated, supersaturated or unsaturated?

Exercise 4) What is the mass percentage of NaCl in a solution containing 1.50 g of NaCl in 50.0 g of water? 5) What is the molality of a 5.86 M ethanol (C2H5OH) solution whose density is 0.927 g/ml? 6) What is the mole fraction of HCl in a solution of hydrochloric acid that has 36% HCl by mass? What is its molality? What is its molarity? The density of the acid solution is 1.305 g/ml

Exercise 7) Calculate the molalithy, molarity and mole fraction of FeCl3 in a 28.8 mass % aqueous solution (with density of 1.280 g/ml) 8) An automobile antifreee mixture is made by mixing equal volumes of ethylene glycol (d=1.114 g/ml; MW = 62.07 g/mol) and water (d=1.00 g/ml) at 20 C. The density of the resulting mixture is 1.070 g/ml. a) % volume c) molarity e) mole fraction b) % mass d) molality

V EG = V W (in ml) %V = V EG V EG + V W = 50.0% %mass = g EG g EG + g W = d EG *V EG ( d EG *V ) EG + ( d W *V ) W %mass = d EG *V EG ( d EG *V ) EG + ( d W *V ) EG %mass = d EG *V EG = ( d EG + d W )V EG d EG ( d EG + d ) = 52.7% W

M = n EG V total = M = M = MW EG n EG ( V EG + V ) W *10 3 g EG *10 3 = V EG + V W d EG *V EG *10 3 MW EG * ( V EG + V ) W d EG *V EG *10 3 MW EG V EG + V W M = d EG *V EG *10 3 MW EG * 2V EG = d EG *10 3 2MW EG = 8.97M

m = n EG g W = m = n EG d W *V W *10 3 g EG MW EG d W *V W *10 = 3 m = d EG *V EG *10 3 MW EG *( d W *V ) W d EG *V EG MW EG d W *V W *10 3 m = d EG *V EG *10 3 MW EG *( d W *V EG *) = d EG *10 3 MW EG * d W =17.95m

X EG = X EG = X EG = n EG n EG + n W g EG d EG *V EG MW EG MW = EG g EG g + W d EG *V EG + d W *V W MW EG MW W MW EG MW W d EG *V EG MW EG d EG *V EG + d *V W W MW EG MW W

X EG = d EG *V EG MW EG d EG *V EG * MW W + MW EG * d W *V W MW EG * MW W X EG = d EG *V EG d EG *V EG * MW W + MW EG * d W *V W MW W X EG = X EG = X EG = MW W * d EG *V EG d EG *V EG * MW W + MW EG * d W *V W MW W * d EG *V EG d EG *V EG * MW W + MW EG * d W *V EG MW W * d EG d EG * MW W + MW EG * d W = 0.244

Errors in Chemical Analysis Chapter 3

Significant Figures All non-zero digits Zero digits are significant when Between non-zero digits To the left of the decimal point To the right of the decimal point, after/to the right of a non-zero digit/s

Arithmetic Addition/Subtraction Least decimal place Multiplication/Division Least sigfig Logarithms

Inherent errors are part of the world we live in. Because of this, it is impossible to perform a chemical analysis that is totally free of errors of uncertainties. We can only hope to minimize errors and estimate their size with acceptable accuracy. Error can denote two meanings: 1). Difference between measured value and true value Accuracy 2). Estimated uncertainty of a measurement Uncertainty Mean average Median central value Trial Ppm Fe 3+ 1 20.3 2 19.5 3 19.4 4 19.8 5 20.1 6 19.6

Replicates are samples of the same size that are carried through an analysis in exactly the same way Precision describes the reproducibility of measurements in other words, the closeness of results that have been obtained in exactly the same way. Evaluated as Standard deviation, variance or coefficient of variation

Accuracy indicates the closeness of the measurement to the true or accepted value and is expressed by the error. Evaluated as Absolute Error (E) or Relative Error (E R ) Uncertainty A parameter associated with the result of a measurement, that characterises the dispersion of the values that could reasonably be attributed to the measurand Evaluated as Absolute Uncertainty (u) or Relative Uncertainty (u R ) Eurachem/CITAC Guide. Quantifying Uncertainty in Analytical Measurement. 2 nd Edition. 2000

Types of Error Systematic Error or Determinate Error Is repeatable, discoverable and corrected Uncalibrated instruments Random Error Limitations of our ability Discipline and consistency Gross Errors Occurs occasionally, results in outliers

Systematic Errors can arise from (1) Instrument error, (2) Method error or (3) Personal error. Systematic Error INSTRUMENT ERROR Instruments can have low tolerances and temperature sensitive Power supply may fluctuate Reagents can produce reactions with the instrument thus inducing error Electrical Noise Instrument Calibration Background Subtraction

Systematic Errors can arise from (1) Instrument error, (2) Method error or (3) Personal error. Systematic Error METHOD ERROR Non-ideal chemical and physical behavior of reagents Kinetics Equilibrium Instability Side reactions Incomplete digestions Use of Standard Reference Materials Independent Analysis Blanks

Systematic Errors can arise from (1) Instrument error, (2) Method error or (3) Personal error. Systematic Error PERSONAL ERROR Due to personal biases Color perception Reading of pointers and marks Care and Self-discipline OCness

Systematic Errors can be constant or proportional Systematic Error CONSTANT: Buret reading Solubility Titration Increase sample size! PROPORTIONAL Due to contamination/ interferences Quality Assurance and Calibration

Random errors arise from limitations on our ability to make physical measurements and on natural fluctuations Random Error Random reading of scale and instrument use. Random Background Noise Sampling Use of Statistics to ESTIMATE the amount of error.

Uncertainty is propagated during a chemical analysis y( x ) i u( y) = y x i 2 u( x ) 2 i

Uncertainty is propagated during a chemical analysis For addition and subtraction y = x 1 + x 2 ( ) = u( x ) 1 u y For multiplication and division y = x 1 * x 2 y = x 1 x 2 %u R y [ ] 2 + [ u( x )] 2 2 [ ] 2 + [%u ( x )] 2 R 2 ( ) = %u ( x ) R 1

Real rule of significant figures: The first uncertain figure in the answer is the last significant figure